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SA-IAL-S2-CD-0074 marksL3 ExamCalculatorNormal approximations

X\sim B(50,0.4)

. Use a normal approximation to find

P(X\ge25)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-MOM-0044 marksL3 ExamCalculatorTilting

A uniform plank

AB

6

m long and of mass

20

kg, rests on supports at

C

and

D

, where

AC=DB=1

m. A man of mass

70

kg walks from

D

towards

B

. Find his distance from

A

when the plank is about to tilt, to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-PM-PAR-0033 marksL3 ExamNon-calculatorIntersections

The curve

x=t^2

y=2t

meets the line

y=x-3

at two points. Find their

x

-coordinates.

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SA-PROOF-0061 markL3 ExamCalculatorDeduction & exhaustion

In the proof above, the case

n=3k+2

gives

n^2=9k^2+12k+4=3(3k^2+4k+1)+r

. Find

r

Salam Academy Original Practice · Proposed mark scheme

SA-PX-EY-0032 marksL3 ExamCalculatorDefects

A long-sighted person has a near point of

1.0

m. Calculate the power of lens that lets them read a book at

0.25

Salam Academy Original Practice · Proposed mark scheme

SA-PX-VI-0033 marksL3 ExamCalculatorStokes’ law

A steel ball of radius

1.0

mm and density

7800

kg m⁻³ falls through glycerol of density

1260

kg m⁻³ and viscosity

1.4

Pa s. Calculate its terminal velocity in cm s⁻¹.

Salam Academy Original Practice · Proposed mark scheme

SA-ST-PG-0033 marksL3 ExamNon-calculatorMoments

For

G(t)=\frac14(1+2t+t^2)

, find

\text{Var}(X)

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SA-9709-P1-FN3-0054 marksL4 ChallengingCalculatorQuadratic inverses

f(x)=x^2+6x+4

for

x\le-3

. Find

f^{-1}(x)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE-0085 marksL4 ChallengingCalculatorIntersections

Lines

l_1

and

l_2

have equations

\mathbf{r}=\begin{pmatrix}2\\-1\\0\end{pmatrix}+\lambda\begin{pmatrix}1\\2\\1\end{pmatrix}

and

\mathbf{r}=\begin{pmatrix}0\\4\\4\end{pmatrix}+\mu\begin{pmatrix}1\\-1\\-1\end{pmatrix}

. Show that the lines intersect and find the coordinates of the point of intersection.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE-0094 marksL4 ChallengingCalculatorIntersections

Lines

l_1:\ \mathbf{r}=\begin{pmatrix}1\\0\\2\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\-1\end{pmatrix}

and

l_2:\ \mathbf{r}=\begin{pmatrix}3\\1\\0\end{pmatrix}+\mu\begin{pmatrix}1\\-1\\2\end{pmatrix}

. Which statement is true?

Salam Academy Original Practice · Proposed mark scheme

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